where \(A_i\) , \(\omega _i\) , \(\Delta \omega _i\) , \(\phi _i\)  and \(\tau _i\)  denotes the amplitude, fundamental frequency, bandwidth, spectral phase and center time of \(i\) th pulse, respectively. By setting the values of \(\omega _1\)  and \(\omega _2\)  to the transition frequencies \(\omega _{01}\)  and \(\omega _{12}\) , the optimal amplitudes of \(\theta _1(t_f)\)  and \(\theta _2(t_f)\)  can be obtained by scaling the amplitudes \(A_1\)  and \(A_2\) , and the phase conditions can be satisfied by modulating the combined values of \(\phi _1(\omega _{01})-\omega _{01}\tau _1\)  and \(\phi _2(\omega _{12})-\omega _{12}\tau _2\) . Note that the maximum orientation is only obtained when the two pulses do not overlap in frequency space, and therefore two narrow-bandwidth terahertz pulses consisting of multiple cycles will be required to satisfy the criteria of Eqs. (REF ) and (REF ). It implies that the present two-pulse scheme is different from our previous work [1]} using a single-cycle terahertz pulse, for which the rotational excitation involves optical processes governed by high-order Magnus terms, going beyond the present rotational ladder-climbing mechanism.
